Math Problem Statement
Find the angle correct to two decimal places for the lines joining the given points that they make with the positive direction of the x-axis
Solution
To find the angle that a line joining two points makes with the positive -axis, we use the slope of the line and the relationship between slope and angle.
Formula:
The slope of a line is given by: The angle that the line makes with the positive -axis is then calculated using: where is measured in radians or degrees. Ensure the angle is in the correct quadrant based on the signs of and .
Steps:
- Compute the slope using the coordinates of the two points.
- Use the inverse tangent function to find the angle in radians or degrees.
- Adjust to ensure it is in the correct quadrant.
- Round to two decimal places.
Example Input:
Please provide the two points and , and I will calculate the angle for you.
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Math Problem Analysis
Mathematical Concepts
Geometry
Trigonometry
Slope
Coordinate Geometry
Formulas
m = (y2 - y1) / (x2 - x1)
theta = tan^(-1)(m)
Theorems
Inverse Tangent Function
Slope-Angle Relationship
Suitable Grade Level
Grades 9-12